Role of Singular Tori in the Dynamics of Spatiotemporal Nonlinear Wave Systems

被引：29

作者：

Sugny, D. ^{[1
]}

Picozzi, A. ^{[1
]}

Lagrange, S. ^{[1
]}

Jauslin, H. R. ^{[1
]}

机构：

[1] CNRS, Inst Carnot Bourgogne, UMR 5027, F-21078 Dijon, France

来源：

PHYSICAL REVIEW LETTERS | 2009年 / 103卷 / 03期

关键词：

POLARIZATION; MONODROMY;

D O I：

10.1103/PhysRevLett.103.034102

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that the peculiar topological properties inherent to singular tori play a major role in the spatiotemporal dynamics of counterpropagating nonlinear waves. Under rather general conditions, these Hamiltonian wave systems exhibit a relaxation process towards a stationary state. We show that this stationary state converges exponentially towards the singular torus of the associated Liouville-integrable Hamiltonian system in the limit of an infinite medium. The singular torus then appears as an attractor for the infinite dimensional dynamical system, a feature which is illustrated by several key models of spatiotemporal wave interactions.

引用

页数：4

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